WAEC Mathematics 2017 Paper

Concept:For a solid hemisphere, the total surface area includes the curved surface and the flat circular base, so $T.S.A = 3\pi r^2$.The volume of a solid hemisphere is $V = \frac{2}{3}\pi r^3$.Equate the two given quantities and solve for the radius $r$.Explanation:Write the formula for the total surface area of a solid hemisphere.$T.S.A = 3\pi r^2$Write the formula for its volume.$V = \frac{2}{3}\pi r^3$Since the total surface area equals the volume, set the expressions equal.$3\pi r^2 = \frac{2}{3}\pi r^3$Divide both sides by $\pi r^2$.$3 = \frac{2}{3}r$Multiply both sides by $3$.$9 = 2r$Divide both sides by $2$.$r = \frac{9}{2} = 4.5$Therefore, the radius is $4.5$ cm.Answer:$r = 4.5$ cm (Option B).